My reading of Wild Shape has always been that your Str, Dex, and Con become exactly that of the beast you shift into, as part of:
Your game Statistics are replaced by the Statistics of the beast, but you retain your alignment, personality, and Intelligence, Wisdom, and Charisma scores.
Doing a straight "use what's written" approach seems to fit with the general 5E philosophies of reducing at-the-table situational modifiers and of not stacking things.
On the other hand, there are parts of shifting which aren't that simple (for example, retaining proficiencies, which can cause skill and save bonuses to be recalculated). And, there's this:
You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.
In 5th edition, "Ability Score Increase" is explicitly a class feature. "Having increased strength" seems pretty clearly something any physical form can be physically capable of. So, do you keep these increases and add them to those of the selected beast?
I am particularly looking for official rules or rulings, including whether this is the way things should be done for Adventurer's League play. This question is about ability score increases which come from feats rather than just the Ability Score Increase class feature, but the Jeremy Crawford tweet cited is concerned with hit points, which are a different thing, and the accepted answer makes a distinction about parts of the feat only applying during leveling up, which I don't see anywhere in the actual rules.
If there's not a rules-as-written statement anywhere, I'd also be interested in something official which speaks to rules-as-intended, because allowing this doesn't seem particularly out of balance — it still takes a significant character-building option that could go to something else, and the limit of 20 still clearly would apply.
Best Answer
The bonus of ASI is a one-time-only increase to ability scores:
It is not always "on", but happens at certain points in time. After you get those levels, you are not under the effect of the ASI anymore. Thus wild shape will replace your increased scores.